A note on identification and metric issues for skew IRT models

The skew-normal distribution (SND) is a flexible family of densities which preserves some useful properties of the original normal distribution. Some stochastic representations for the SND have beenproposed in the literature. The Henze (H) and Sahu, Branco and Dey (SBD) are the two most used ones. On the other hand, the centered parametrization is useful for inference purposes. The main goals ofthis article are: establish a link between the standard H and SDB skew-normal distributions and use this result to model the latent traits for IRT models. We proved that standard H and SDB distributions are related to each other through a function of the asymmetry parameter and also that they are exactly the same under centered parametrization (CP). Using these results, we showed that the common density obtained through the CP is useful to model the latent traits for unidimensional IRT models. This approach allows to represent asymmetric latent traits behavior and ensures the model identification as well.